We think ourselves now so sophisticated because we know the world isn’t designed, at least not in the way of a human engineer. But there are patterns and the ways of thought which provide some serious understandings of those patterns arising from states of seeming disorder are difficult and are certainly not yet part of the machinery of the human intellect or communal mind, the mind which does the sort of thinking which has made it possible for past “skills for geniuses” to be taught in the elementary schools of mass education within a few centuries of the development of those skills. See Mathematical Models of Human Communities: Randomness for one of a number of discussions I’ve provided of the general topic of order arising from seeming disorder. That same essay also discusses the strange history of long division: “[I]n the 14th century or so, long division was coming into use and was considered to be a topic for mathematical geniuses, well beyond those even of more normal high intelligence. Nowadays, we start learning long division in mass education elementary schools, though many still have trouble with it and some can never master it even to the point of figuring how much per pound a roast costs if 4.5 pounds costs $25.”
I’ve suggested in various writings and in various ways that thoughts are created being, images of that created being but images in a sense similar to: “Men are made in the image of God.” Created being is the manifestation of specific thoughts of God and we learn how to think truly by sharing those thoughts of God, by shaping our minds (but also our hearts and hands) in response to created being and its relationships and actions. Images can be concrete things. Concrete things have abstract created being as well as concrete created being.
One of the main points behind this line of reasoning can be stated: created being is created being is created being. There is a complex network of various streams coming from the truths God manifested as the raw stuff of created being, probably branching out at places and then joining again as it journeys, so to speak, to this very concrete realm of created being, of thing-like being. See this recent essay for a discussion of this general issue in a particular, focused form: Developing Human Minds, Individual and Communal. Pay particular attention to the very simple chart of created being to gain some idea of what I mean about abstract being branching out to more particular forms and joining along the way; many of those branches come together in this world of things. Even relatively simple things, for example—simple lifeforms, are the result of the shaping and the combining of a lesser or greater variety of abstract forms of being.
It would be hardly surprising if various animals have characteristics once claimed for human beings only. I’ve argued that man is unique because of the very complex human brain which is capable of `making up’ a mind. See How Brains Make Up Their Minds by the neuroscientist and philosopher Walter J. Freeman for a discussion of what it means to make up a mind. I go beyond Professor Freeman, or perhaps in a different direction from him, in seeing the human mind as capable of encapsulating what lies around it, even the entire universe and beyond, in the form of what I call a worldview, that is, a complex understanding which is unified and coherent and complete in the way of a world or—still better—all of Creation.
But this human uniqueness, seen in more or less expansive terms, is the result of evolutionary processes and a series of specific events over time. It would be hardly surprising if specific human characteristics, even particular skills of abstract reasoning, could be found even in animals we think to be truly dumb, such as chickens. Chimpanzees can keep objects in mind when those objects are no longer present and and can imagine them as being useful in solving an immediate problem. Birds from the crow family can engage in relatively powerful reasoning processes, as can octopuses.
Now we can learn from this article, Chicks Put Low Numbers on the Left, Just Like Humans, that even relatively dumb birds can not only deal with number concepts but they can order them. That they order them left to right seems to me to probably be an accident of evolution, perhaps a coincidence and perhaps a result of brain structures we’ve shared with the chicken’s line of evolution for tens or even hundreds of millions of years. Such details are important for some purposes but not for mine; at least, these particular details aren’t important for my main point in this essay.
The main point is a joining of the my first line of thought for most of this essay and the reference to some experimental facts discussed quickly in the above paragraph. Neither human beings nor chicks derive numbers, or the ordering of numbers, from some pure realm of abstractions and concepts, a Platonic realm of Ideas. Numbers are in the most concrete of things. Concrete being is shaped from those forms of abstract being we explore by way of mathematics, which is a way of exploring a form of created being with that same form, as physicists probe matter with matter. We can see this clearly with the knowledge of matter and energy and fields which comes from quantum physics. My contention is that this knowledge, mathematical formalisms which are the wavefunctions, is really abstract created being and not `mere’ knowledge. In a similar way, knowledge of numbers and the ordering of numbers, left-to-right or top-to-bottom or other, is actually a particular sort of abstract created being which is present in the concrete being of this mortal realm.
In a similar but more complex and complicated way, the order which arises from seeming chaos can be described in mathematical terms. I contend we are seeing actual created being in those patterns—fixed point phenomena, for example, are a form of abstract being. They are points of stability, f(x)=x, where the function `reproduces’ the input though perhaps in a complex and iterative process. I contend that stability isn’t just something which can happen and then can be modeled by experts in the sciences of dynamic systems. I contend that that stability is a form of created being which is described by “f(x)=x” and is f(x)=x, just as a man can be described as “rational” and rationality is a form of created being which is part of that complex entity, a man.
When we see a system come to order, perhaps by stabilizing around a fixed point (stability is rarely absolute even in simple systems such as pendulums), we could talk of an emergence in that system of that abstract form of created being we know as “stability” or we could talk about a stream of created being which is flowing into that system. I don’t know if one or the other is more right or otherwise more preferable. I do know that the stability of a fixed point isn’t so different from the set of relationships found in Schrodinger’s wavefunction, the set of relationships which are Schrodinger’s wavefunction. Concrete things come from something which can be described in those mathematical formalisms. I’m suggesting we can do no better, at least for now, than to regard those mathematical formalisms as abstract being from which concrete being is shaped; I’m suggesting that mathematical formalisms are a form of created being and not simply descriptions of some form of created being which is currently only describable in terms of those formalisms. It’s a clean way of thinking and talking which may ultimately be wrong or just part of the truth, but it allows us to avoid a lot of gibberish and to develop more unified and complete and coherent understandings. And I contend those understandings are encapsulations of created being, even of Creation, and I mean encapsulations in the same sense as used by the Biblical authors: man is an image of God. Our minds are images of what we recognize as existing, perhaps a very limited environment in the case of early men and perhaps all of Creation to those who share in abstract reasoning—not just philosophers but all of those who are engaged members of a civilization which contains philosophers and physicists and historians and composers of complex music.